Interatomic potentials in solids

Abstract

The following points have been stressed in this brief survey:

• (i) The ground-state energy E is very naturally considered as E[ϱ(r{{ℓ}}], p being the electron density and {ie113-1} the totality of nuclear sites.

• (ii) Whereas the wave equation gives a delocalized ϱ(r{{ℓ}}) inevitably (and only determines localized distributions uniquely in a special case like NaCl), physical and chemical intuition can go into choice of localized densities, which will then often allow decomposition into pair, and many body terms.

• (iii) Even for small displacements from equilibrium, however, as in for example lattice vibrations, such localized electron distributions must deform as the nuclei move.

• (iv) For the classical ionic model, the localized picture corresponds to the Heitler-London crystal wave function of cations and anions, which leads in turn to a superposition property of first-order density matrices. The additivity property of polarizabilities follows as a consequence.

• (v) Bonds afford a valuable description of electron density and hence force fields in group IV semiconductors, partially ionic 3–5 compounds, and metals with directional charge distribution (e.g. Be (30-32) Fe, Cr).

• (vi) For small displacements, an exact formal theory exists. But this requires the concept of a tensor charge density; this has not yet been made quantitative though.

• (vii) Some progress is possible for large displacements, but presently only through limited cohesive energy inversion at a first-principle level. Otherwise, modelling or phenomenology is still essential in this important area. This latter problem will be taken up in several later chapters in the book.